Construction of the Wigner–Racah algebra of the group $SU_3$

A method is developed for constructing the Wigner–Racah algebras of the groups $SU_n$ on the basis of their isomorphism with the algebras of generating invariants. Graphanalytical rules are formulated that enable one to write down immediately any quantity in the Wigner–Racah algebra of $SU_3$ and find its numerical value. The resulting closed computational formalism can be regarded as a direct generalization to the group $SU_3$ of the ordinary theory of angular momenta.